Plithogenic MOORA

Cells. In crisp MOORA every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I), falsity (F). One criterion is taken as dominant, with a contradiction degree of zero; how strongly the other criteria oppose this dominant criterion is given by a fixed, per-criterion contradiction degree between 0 and 1. This degree is the same for every alternative under a given criterion and does not vary from one alternative to another. Criterion weights are an input separate from the contradiction degree and arrive from outside as crisp numbers.

Scale equalisation. Crisp MOORA divides each column by the square root of the sum of its squared values. Here every cell is first adjusted by its own criterion's contradiction degree: truth is pulled upward towards the dominant criterion, while indeterminacy and falsity are shrunk by the same proportion. A single score is then drawn from this adjusted triple (truth positively weighted, indeterminacy weighted twice and negatively, falsity negatively weighted). Since the score can fall between −1 and 1, it is shifted by adding 1, and is then normalised, as in crisp MOORA, by dividing by the square root of its own column magnitude. The triple is not reversed for a cost criterion; as in crisp MOORA, the direction difference is carried by sign in the addition-and-subtraction step that follows.

Ratio system. The normalised, shifted scores are weighted; the sum over "more is better" criteria has the sum over "less is better" criteria subtracted from it. This is exactly the same operation as crisp MOORA's ratio system; the only difference is that the input has already been reduced to a T-I-F score through contradiction adjustment.

Result and defuzzification. Contradiction adjustment and score extraction are themselves the defuzzification, and they take place at MOORA's first step, not at its end. DecisionMind also lists the reference-point approach in this family as a step, but that step simply copies the ratio system's score as it stands; it produces no separate calculation of its own. In effect, therefore, the only approach that actually operates in this extension is the ratio system.

DecisionMind fixes the contradiction adjustment, the score function and the vector normalisation in classical Plithogenic MOORA. Weights and contradiction degrees are taken from outside and separately from one another; the method generates neither.

The output is a net score and a rank, as in crisp MOORA, and is read the same way: it is neither a percentage nor a probability, and it is not compared with a different analysis. The difference is here: beneath the score lie both T-I-F indeterminacy and an assumption about the degree of contradiction between criteria. In the illustrative example below, this assumption reverses the ranking of A1 and A3 with a small change; A2 stays ahead in every scenario.

Thus instead of writing:

"Plithogenic MOORA gives a more reliable result because it also accounts for contradiction"

the report should read:

"The contradiction degree between criteria has been given under the following assumption; A2 has the highest net score, while the ranking of A1 and A3 is sensitive to this assumption"

Taking contradiction into account does not automatically make the result more correct; it merely makes visible which assumption is influencing the ranking.

Use this extension when your criterion scores are given as a truth-indeterminacy-falsity triple, and some criteria carry information that is more "independent", or more "in conflict", than others. If the T-I-F triple alone is sufficient and no such dominance-contradiction relationship exists among the criteria, neutrosophic MOORA (n-moora) is already sufficient; the plithogenic form adds one further assumption, and if that assumption is given without justification it creates a spurious distinction.

Converting a measured criterion into a T-I-F triple is manufacturing indeterminacy, not modelling it. If the table is mixed, DecisionMind requires a single data type. The exit condition is the same as for crisp MOORA: if no compromise is acceptable on one criterion, this extension too is compensatory and will not eliminate anything below a threshold.

Violating the value space. Every cell must be a valid T, I, F triple, and a contradiction degree must be declared for every criterion; running the method with a missing or invented contradiction degree invalidates it.

Assigning the contradiction degree without justification. In the illustrative example, raising C2's contradiction degree from 0.33 to 0.55 reverses the ranking of A1 and A3. If this degree is given "by feel", the ranking becomes a feeling too; the degree must rest on a measurable justification for how independent, or how overlapping, a criterion's information is relative to the dominant criterion.

Choosing the dominant criterion arbitrarily. Which criterion is taken to have zero contradiction is a decision and must be justified in the report; if the dominant criterion changes, the contradiction degrees of the other criteria must be reconsidered too.

Treating the reference-point approach as a genuine second method. In this extension the reference-point step copies the ratio system's score and performs no independent calculation. Presenting the result as "confirmed by two methods" is wrong; in effect only one approach is at work.

The governing principle is this:

The contradiction degree is a criterion's share of independence or contradiction, drawn from measurable ground; an unjustified figure also makes the ranking produced by the ratio system unjustified.